It is observed that three-dimensional Gödel black holes can be promoted to exact string theory backgrounds through an orbifold of an hyperbolic asymmetric marginal deformation of the SL(2,R) WZW model. Tachyons are found in the spectrum of long strings. Uplifting these solutions in type IIB supergravity, extremal black holes are shown to preserve one supersymmetry in accordance with the BTZ limit. We also make connections with some recently discussed warped black hole solutions of topologically massive gravity, showing that they actually correspond to quotients of spacelike squashed AdS_3.

In all the odd dimensions which allow Majorana spinors, we consider a gravitational Lagrangian possessing local Poincare invariance and given by the dimensional continuation of the Euler density in one dimension less. We show that the local supersymmetric extension of this Lagrangian requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. By maximal, we mean that in the right hand side of the anticommutator of the Majorana super charge appear all the possible central charges. The resulting action defines a Chern-Simons gauge theory for the maximal extension of the super-Poincare algebra. In these dimensions, we address the same problem for the AdS invariant gravity and we derive its supersymmetric extension for the minimal super-AdS algebra. The connection between both models is realized at the algebraic level through an expansion of their corresponding Lie super algebras. Within a procedure consistent with the expansion of the algebras, the local supersymmetric extension of the Poincare invariant gravity Lagrangian is derived from the super AdS one.

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We explicitly calculate the induced gravity theory at the boundary of an asymptotically Anti-de Sitter five dimensional Einstein gravity. We also display the action that encodes the dynamics of radial diffeomorphisms. It is found that the induced theory is a four dimensional conformal gravity plus a scalar field. This calculation confirms some previous results found by a different approach.